Can a Spinning Astronaut Use a Tethered Bowling Ball to Gain Motion in Space?

[moses1592]

Consider this scenario: two astronauts are floating in outer space with no other frame of reference other than themselves. Relative to one another they are stationary and have no motion between them, except that one astronaut is spinning at one revolution per second. The astronaut that is spinning is tightly holding a bowling ball against his chest. The bowling ball is also tethered to him on a long cable.

The spinning astronaut has potential (muscle) energy in his body which allows him to toss the bowling ball if he desires. He also has potential energy in his spin. If he slowly releases the bowling ball on the tether his rotation will slow down but he will remain stationary and won't feel a force of acceleration. If he pulls it back in then his spin will increase back to its original 1 rotation per second. Let's say he violently throws the ball as hard as he can.

The moment he let's go he will be pushed and begin moving backwards as the ball proportionally moves forward, except he will still be spinning while the ball is moving. I believe the ball Will have some rotation as well. This of course will be negated (at least partially) when the ball reaches the end of the tether and recoils.

Will this inevitable recoil always 100% negate any relative motion created by throwing the ball? Would this act alter the rotation rate of the astronaut since energy was spent in the act of the throw/recoil? I know any time an object/system expends energy it loses a tiny amount of mass, but for this scenario assume it's so small as to be negligible.

In closing, is there any way for the spinning astronaut to use his tethered bowling ball, potential muscle and/or rotational energy to gain motion relative to his buddy astronaut without sacrificing mass or cutting the tether?

 

[Nugatory]

Think about the implications of momentum conservation here...

 

[DrStupid]

In closing, is there any way for the spinning astronaut to use his tethered bowling ball, potential muscle and/or rotational energy to gain motion relative to his buddy astronaut without sacrificing mass or cutting the tether?

He will gain motion relative to his buddy due to gravitational attraction. Without sacrificing reaction mass all he can do is using the bowling ball to increase this effect.